# James H. Nolen

- Associate Professor of Mathematics

**External address:**243 Physics Bldg, Durham, NC 27708

**Internal office address:**Box 90320, Durham, NC 27708-0320

**Phone:**(919) 660-2862

**Office Hours:**

Mondays, 3:30-5:00

Wednesdays, 10:30-12:00

### Research Areas and Keywords

##### Analysis

##### Biological Modeling

##### PDE & Dynamical Systems

##### Physical Modeling

##### Probability

I study partial differential equations and probability, which have been used to model many phenomena in the natural sciences and engineering. In some cases, the parameters for a partial differential equation are known only approximately, or they may have fluctuations that are best described statistically. So, I am especially interested in differential equations modeling random phenomena and whether one can describe the statistical properties of solutions to these equations. Asymptotic analysis has been a common theme in much of my research. Current research interests include: reaction diffusion equations, homogenization of PDEs, stochastic dynamics, interacting particle systems.

### Fellowships, Supported Research, & Other Grants

NSF Postdoctoral Research Fellowship awarded by National Science Foundation (2006 to 2008)

Nolen, J. "Normal approximation for a random elliptic equation." *Probability Theory and Related Fields* 159.3-4 (2014): 661-700.
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Nolen, J. "Normal approximation for a random elliptic equation." *Probability Theory and Related Fields* (2013): 1-40.
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Hotz, T, Huckemann, S, Le, H, Marron, JS, Mattingly, JC, Miller, E, Nolen, J, Owen, M, Patrangenaru, V, and Skwerer, S. "Sticky central limit theorems on open books." *The Annals of Applied Probability* 23 (2013): 2238-2258. (Academic Article)
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Mellet, A, and Nolen, J. "Capillary drops on a rough surface." *Interfaces and Free Boundaries* 14.2 (2012): 167-184.
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Nolen, J, Roquejoffre, J-M, Ryzhik, L, and Zlatoš, A. "Existence and Non-Existence of Fisher-KPP Transition Fronts." *Archive for Rational Mechanics and Analysis* 203.1 (2012): 217-246.
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Hamel, F, Nolen, J, Roquejoffre, J-M, and Ryzhik, L. "A short proof of the logarithmic Bramson correction in Fisher-KPP equations (Accepted)." *Networks and Heterogeneous Media* (2012). (Academic Article)

Matic, I, and Nolen, J. "A Sublinear Variance Bound for Solutions of a Random Hamilton-Jacobi Equation." *Journal of Statistical Physics* 149.2 (2012): 342-361.
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Nolen, J. "A central limit theorem for pulled fronts in a random medium." *Networks and Heterogeneous Media* 6.2 (2011): 167-194.
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Cardaliaguet, P, Nolen, J, and Souganidis, PE. "Homogenization and Enhancement for the G-Equation." *Archive for Rational Mechanics and Analysis* 199.2 (2011): 527-561.
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Nolen, J, and Novikov, A. "Homogenization of the G-equation with incompressible random drift in two dimensions." *Communications in Mathematical Sciences* 9.2 (2011): 561-582.